One-loop Matching Factors for Singlet Quasi-Parton Distribution Functions in the Hybrid-Ratio Scheme

TL;DR

This paper calculates one-loop matching kernels between PDFs and quasi-PDFs for various partons within the hybrid-ratio scheme, confirming key properties like flavor number conservation and moment equivalence through numerical analysis.

Contribution

It provides the first one-loop matching kernels for singlet quasi-PDFs in the hybrid-ratio scheme, demonstrating conservation laws and moment relations.

Findings

Quark number conservation for each flavor is maintained.

The second moments of quasi-PDFs and PDFs are equal.

Numerical validation using CTEQ14 data confirms theoretical results.

Abstract

The one loop matching kernels between parton distribution functions (PDFs) for parton $i=u,d,s,g$ and their corresponding quasi-PDFs are computed at one loop in the hybrid-ratio scheme. We found that, in addition to the conservation of the quasi-quark number for each flavor, the second moment $\langle x \rangle_{\tilde{i}}=\langle x \rangle_i$ of quasi-PDF of parton $i$ (denoted as $\tilde{i}$) and PDF of parton $i$ is the same in our approach. This is demonstrated numerically using the CTEQ14 global analysis as input.